Sr Examen

Otras calculadoras

(cos(2x)-sqrt(2)*sin(x-1))/tg(x-1)=0 la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

v

Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

Ha introducido [src]
             ___               
cos(2*x) - \/ 2 *sin(x - 1)    
--------------------------- = 0
         tan(x - 1)            
$$\frac{- \sqrt{2} \sin{\left(x - 1 \right)} + \cos{\left(2 x \right)}}{\tan{\left(x - 1 \right)}} = 0$$
Solución detallada
Tenemos la ecuación
$$\frac{- \sqrt{2} \sin{\left(x - 1 \right)} + \cos{\left(2 x \right)}}{\tan{\left(x - 1 \right)}} = 0$$
cambiamos
$$\frac{- \sqrt{2} \sin{\left(x - 1 \right)} + 2 \cos^{2}{\left(x \right)} - \tan{\left(x - 1 \right)}}{\tan{\left(x - 1 \right)}} = 0$$
$$\frac{- \sqrt{2} \sin{\left(x - 1 \right)} + 2 \cos^{2}{\left(x \right)}}{\tan{\left(x - 1 \right)}} - 1 = 0$$
Sustituimos
$$w = \sin{\left(x - 1 \right)}$$
Tenemos la ecuación:
$$\frac{- \sqrt{2} \sin{\left(x - 1 \right)} + 2 \cos^{2}{\left(x \right)}}{\tan{\left(x - 1 \right)}} - 1 = 0$$
Usamos la regla de proporciones:
De a1/b1 = a2/b2 se deduce a1*b2 = a2*b1,
En nuestro caso
a1 = 2*cos(x)^2 - sqrt(2)*sin(-1 + x)

b1 = tan(-1 + x)

a2 = 1

b2 = 1

signo obtendremos la ecuación
$$- \sqrt{2} \sin{\left(x - 1 \right)} + 2 \cos^{2}{\left(x \right)} = \tan{\left(x - 1 \right)}$$
$$- \sqrt{2} \sin{\left(x - 1 \right)} + 2 \cos^{2}{\left(x \right)} = \tan{\left(x - 1 \right)}$$
Abrimos los paréntesis en el miembro izquierdo de la ecuación
2*cosx^2 - sqrt2sin-1+x = tan(-1 + x)

Abrimos los paréntesis en el miembro derecho de la ecuación
2*cosx^2 - sqrt2sin-1+x = tan-1+x

Transportamos los términos libres (sin w)
del miembro izquierdo al derecho, obtenemos:
$$- \sqrt{2} \sin{\left(x - 1 \right)} + 2 \cos^{2}{\left(x \right)} + 1 = \tan{\left(x - 1 \right)} + 1$$
Esta ecuación no tiene soluciones
hacemos cambio inverso
$$\sin{\left(x - 1 \right)} = w$$
Tenemos la ecuación
$$\sin{\left(x - 1 \right)} = w$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$x - 1 = 2 \pi n + \operatorname{asin}{\left(w \right)}$$
$$x - 1 = 2 \pi n - \operatorname{asin}{\left(w \right)} + \pi$$
O
$$x - 1 = 2 \pi n + \operatorname{asin}{\left(w \right)}$$
$$x - 1 = 2 \pi n - \operatorname{asin}{\left(w \right)} + \pi$$
, donde n es cualquier número entero
Transportemos
$$-1$$
al miembro derecho de la ecuación
con el signo opuesto, en total:
$$x = 2 \pi n + \operatorname{asin}{\left(w \right)} + 1$$
$$x = 2 \pi n - \operatorname{asin}{\left(w \right)} + 1 + \pi$$
sustituimos w:
Gráfica
Suma y producto de raíces [src]
suma
0
$$0$$
=
0
$$0$$
producto
1
$$1$$
=
1
$$1$$
1
Respuesta numérica [src]
x1 = -97.9601685880785
x2 = 93.6769832808989
x3 = -89.3722481271894
x4 = -51.6731362841119
x5 = -57.9563215912915
x6 = -41.4115008234622
x7 = 49.6946861306418
x8 = 65.4026493985908
x9 = 2.5707963267949
x10 = 153.367243699105
x11 = -47.6946861306418
x12 = -82.2522053201295
x13 = 96.8185759344887
x14 = -0.570796326794897
x15 = -64.2395068984711
x16 = -38.2699081698724
x17 = 87.3937979737193
x18 = -75.9690200129499
x19 = -85.3937979737193
x20 = 99.9601685880785
x21 = -91.6769832808989
x22 = -44.553093477052
x23 = 52.8362787842316
x24 = -63.4026493985908
x25 = -25.7035375555132
x26 = -9.99557428756428
x27 = -60.261056745001
x28 = -61.9574253597328
x29 = 30.0082727092227
x30 = 80.2737551666594
x31 = 33.9867228626928
x32 = -88.5353906273091
x33 = 90.5353906273091
x34 = -32.8235803625731
x35 = 15.1371669411541
x36 = 86.556940473839
x37 = -45.3899509769323
x38 = -72.8274273593601
x39 = 73.9905698594798
x40 = 48.8578286307615
x41 = 59.1194640914112
x42 = 84.2522053201295
x43 = -7.69083913385479
x44 = -11.6919429022961
x45 = 62.261056745001
x46 = -17.9751282094757
x47 = 4.87553148050438
x48 = 42.5746433235819
x49 = -1.4076538266752
x50 = 36.2914580164023
x51 = 18.2787595947439
x52 = -95.655433434369
x53 = -13.9740244410344
x54 = -31.9867228626928
x55 = 92.8401257810186
x56 = 27.7035375555132
x57 = -69.6858347057703
x58 = 21.4203522483337
x59 = 55.9778714378214
x60 = 69.9894660910385
x61 = 77.9690200129499
x62 = -101.938618741549
x63 = -53.9778714378214
x64 = -22.5619449019235
x65 = -35.1283155162826
x66 = 32.290354247961
x67 = 40.2699081698724
x68 = -79.1106126665397
x69 = -28.845130209103
x70 = 71.6858347057703
x71 = -3.71238898038469
x72 = 26.0071689407814
x73 = -20.257209748214
x74 = 5.71238898038469
x75 = -66.5442420521806
x76 = 23.7250874020431
x77 = 76.2726513982181
x78 = 8.85398163397448
x79 = 43.4115008234622
x80 = 11.9955742875643
x81 = 46.553093477052
x81 = 46.553093477052